Multivariate Granger Causality (Barrett 2010)

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Transcript of Multivariate Granger Causality (Barrett 2010)

Multivariate Granger Causality Spectral Domain Granger Causality Trace or Det? Adam Barrett, Lionel Barnett, Anil Seth Ideas Univariate error when using past x AND y error when using past x ONLY Multivariate error when using past x AND y error when using past x ONLY What scalar do we want? Choices Causal Density trvMVGC MVGC Entropy No such analogue for = uncertainty in a given b Marginality No such analogue for Let x be a scalar; then, Stability determinant -> biased by zero eigenvalue? / Key identity: Set of variables Want to look at whole network Causal density from all subsets of size kto all subsets of size rgiven the rest Bipartition causal density from all subsets of size kto all subsets of size n-k Scaled causal density from all subsets of size kto all subsets of size s-k think "bcd" but subset of data Tripartition causal density from all subsets of size kto all subsets of size s-kfor all total sets of size s Bundled Connections ONE transmission trace/det is 5 on 5max eigenvalue is best combinationcanonical AR? Constraints known 0 how to add zeros to A? estimate x given only weighted sum of y